In this Appendix we briefly outline the scheme used to numerically generate the soliton gases presented in Appendix . This procedure is based on [1]} and was originally used to generate the numerical synthesis of soliton and breather gases for the focusing NLS equation in [2]}, [3]}. The modification of this scheme for the generation of KdV soliton gas adopted here has been developed in [4]}; we refer the interested reader to the latter reference for an in depth presentation.
